We present a method to perform the non-rigid matching of two 3D medical images, which is fast and fully automated. We illustrate this method in several applications, such as inter-patient registration, cardiac image sequence analysis, and the automatic registration with anatomical atlases, which we identify as currently important challenges for medical image processing. Several interesting inter-patient matching methods have been proposed recently, showing the interest of such techniques, but whose computation time is still prohibitive for practical clinical applications. The main interest of our methods is to perform a "satisfying" non-rigid matching of large image volumes within only several tens of minutes on a conventional workstation. We describe our method as based on "demons" (in the sense of Maxwell's demons) which locally deform the model to push it into a mold, as opposed to more traditional "attractor" based deformable model techniques. Finally, we present experiments on real data, and discuss two current limitations of our technique: the sensitivity to initial positioning, and to intensity variations between images.